Progress in digital imaging hardware design has introduced digital imaging sensors having a dramatically increased number of pixels, or pixel density (i.e., having an increase in the sensor's resolution). While beneficial for many reasons, this results in the size of each pixel becoming smaller and smaller and, therefore, the sensor output signal's susceptibility to noise becoming greater and greater.
In order to attenuate the noise in the most efficient way, it is important that proper modeling of the noise is considered during digital image processing. However, modeling of noise can be difficult since, when utilizing, for example, a digital camera, the images are likely taken under different illumination conditions and different ambient temperatures. In addition, the digital imaging sensor itself may apply different exposure and/or analogue gain settings, or the like. In other words, the noise that results from digital sensing can vary from image to image. Because of inherent photoelectric conversion, the noise is predominantly signal-dependent. A single non-adaptive image processing filter may, therefore, not be useful for all pictures taken under these varying conditions.
Despite this, current filtering algorithms typically assume independent stationary noise models (i.e., signal-independent), and even where a signal-dependent model is assumed, the correct parameters for the noise are often not specified.
Recently, several complete models have been proposed, which explicitly take into account most of the elements that can potentially contribute to the sensor's noise (e.g., dark signal level, Fixed-Pattern Noise, Shot-noise Photonic (Poissonian noise), dark current noise, dark current non-uniformity, photo-response non-uniformity, amplifier noise, circuit noise, thermal noise, pixel cross-talk, correlated double sampling, quantization noise, chromatic conversions, etc.). (See R. Costantini and S. Süsstrunk, “Virtual Sensor Design”, Proc. IS&T/SPIE Electronic Imaging 2004: Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications V, 2004, Vol. 5301, pp. 408-419; H. Wach and E. R. Dowski, Jr., “Noise modeling for design and simulation of computational imaging systems”, Proceedings of SPIE—Volume 5438 Visual Information Processing XIII, Zia-ur Rahman, Robert A. Schowengerdt, Stephen E. Reichenbach, Editors, July 2004, pp. 159-170 (referred to hereinafter as “Wach”); and A. J. Blanksby and M. J. Loinaz, “Performance analysis of a color CMOS photogate sensor,” IEEE Trans. Electron Devices, vol. 47, no. 1, pp. 55-64, January 2000). While these proposed models provide an accurate modeling of each individual contributor to the noise, the large number of parameters contemplated by these complex models makes them eventually unpractical for modeling the overall sensor's noise. Some of the model parameters may implicitly depend on other parameters (posing serious limitations to their estimation, as it is often not possible to estimate many parameters simultaneously with sufficient precision), and some may belong to the inner-workings of the sensor itself and, therefore, may not be known by other than the sensor's manufacturer. In practice, it is thus arguably impossible to achieve any faithful approximation of the overall sensor's noise by means of these much-articulated models. Further, these models treat color channels separately, obtaining different noise parameters for different channels.
In addition, most research literature available on sensor noise analysis was developed within the electronic engineering community and typically comes to conclusions and models which are useful and significant mainly for the purpose of electronic hardware design and integration (e.g., dimensioning of the device, interfacing, shielding, etc.). (See H. Tian, B. Fowler, and A. El Gamal, “Analysis of Temporal Noise in CMOS Photodiode Active Pixel Sensor,” IEEE Journal of Solid-State Circuits, vol. 36, no. 1, pp. 92-101, January 2001). The literature provides results that are of a global nature (i.e., provides noise figures which are valid and accurate for the whole sensor). However, such global noise estimates are rough when applied to an individual pixel of the sensor. These models, therefore, are inadequate for high-quality image processing applications, such as de-noising or de-blurring, since these techniques require accurate pointwise (i.e., pixelwise) knowledge of the noise, in order to properly restore the image details.
A need, therefore, exists for a more accurate and usable noise model that can be placed in the imaging chain for use in de-noising, de-blurring, and other digital image processing tasks (e.g., color interpolation, sharpening, etc.).